In order to compute the Casimir energy, we proceed with the usual techniques
of quantum fields in curved spacetimes [1]}. From the
energy-momentum tensor for the field,
\(T_{\mu \nu }\left[ \psi (\vec{k}),\psi ^{\ast }(\vec{k})\right] =\partial _{\mu }\psi \partial _{\nu }\psi ^{\ast }-\frac{1}{2}g_{\mu \nu }g^{\rho \sigma }\partial _{\rho }\psi \partial _{\sigma }\psi ^{\ast }~, \) 
